# The space of $p$-adic norms

The 1963 paper by Goldman and Iwahori The space of $$p$$-adic norms deals with the space of norms on a finite dimensional vector space $$E$$ over a locally compact complete discrete valuation field $$K$$. I was wondering if the case when $$E$$ is infinite dimensional has appeared in the literature.

It looks that in the infinite dimensional case the space of norms should also have similar properties. It should be a metric space, complete, CAT(0), its apartments are isomorphic to a Banach space of bounded sequences with supremum norm...

Question Is there a generalisation of the paper "The space of $$p$$-adic norms" to the infinite dimensional setting?